Using Einstein's photoelectric equation we can write,
For first case:
hν=ϕ+e(2VS)...(1)
For second case:
h2ν=ϕ+e(VS)...(2)
Using value of e(VS) from equation(2) in equation(1), we can write,
hν=ϕ+21(2hν−ϕ)
⇒hν=ϕ+4hν−2ϕ
⇒2ϕ=43hν
⇒ϕ=23hν
As we know, ϕ=hν0
Therefore, ν0=23ν